Question

Find the limit of the function algebraically.

limit as x approaches negative six of quantity x squared minus thirty six divided by quantity x plus six.

Answer 1

-12

Explanation:

`\lim_(x \to \ -6) (x^2-36)/(x+6)`

We factor the numerator and try to simplify the fraction as much as we can.

`x^2-36 = x^2 - 6^2`

Apply a^2 - b^2 formula (a+b)(a-b)

`x^2-36 = x^2 - 6^2=(x+6)(x-6)`

`\lim_(x \to \ -6) ((x+6)(x-6)/(x+6)`

Cancel out x+6 from top and bottom

`\lim_(x \to \ -6)(x-6)`

Plug in -6 for x

-6-6 = -12

Answer 2

`lim_(x \rightarrow -6) (x^2-36)/(x+6) \\ =lim_(x \rightarrow -6) ((x-6)(x+6))/(x+6) \\ =lim_(x \rightarrow -6) (x-6) \\ =-6-6=-12`